Excerpts from an OT DM article - which also touches on Peter and HM's relationship:
'She has always been close to Peter and admires the way he and his sister Zara handled themselves as grandchildren of the monarch but without royal titles,' says an old friend of the Queen.
She thinks Peter especially has inherited the resilience that is so characteristic of Anne. She sees him as dependable.'
Prince Philip shared this affection and regarded Peter, outdoorsy and sporty, as the most sensible and level-headed of all his grandchildren.
At Gordonstoun, the tough Scottish school where Peter was head boy or 'guardian', as it was called, he wore his royal connections lightly. As Anne famously remarked of Peter and Zara: 'They're not royal. The Queen just happens to be their grandmother.' Even when Anne's marriage to Peter's father, Captain Mark Phillips, was disintegrating, home life at Gatcombe continued relatively untroubled.
One afternoon when she was being cuddled on her grandmother's knee, 18-month-old Zara took hold of the Queen's necklace and broke the string, scattering the priceless pearls over the carpet. 'Granny' voiced no complaint other than a grunt of exasperation, then got down on her hands and knees and, with Peter helping her, picked them up.
Not even the break-up of Peter's marriage to Canadian Autumn Kelly, which ended last year after 13 years and two children, dented the special relationship between grandmother and first grandchild. And you certainly won't find Peter Phillips giving credential-burnishing interviews about his relationship with his grandmother.